Dynamic IP RouterTables Using Highest Priority Matching

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Dynamic IP Router-Tables Using Highest Priority
Matching

• Haibin Lu. Sartaj Sahni
• Computers and Communications, 2004. Proceedings.
  ISCC 2004. Ninth International Symposium on
  , Volume 2 , 28 June-1 July 2004

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Outline

• Preliminaries
• Nonintersecting Highest Priority Rule Tables
  (NHPRTs) BOB
• Highest Priority Prefix Table (HPPTs) PBOB
• Longest Matching Prefix Tables (LMPTS) LMPBOB
• Experiment and conclusion

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Preliminaries

• Def1 Let ru, v and sx, y be two ranges. R
  and s are disjoint iff
• rnsØ. R and s are nested iff one
  of the ranges is contained
• within the other. r and s
  intersect iff r and s have a nonempty
• intersection that is different
  from both r and s
• Def2 The range set R is nonintersecting iff
  there is no pair of
• ranges r and s ? R such that r
  and s intersect
• Def3 Let R be a range set, ranges(d, R)(or
  simply ranges(d) when
• R is implicit) is the subset of
  ranges of R that match the
• destination address d. hpr(d) is
  the highest-priority range in
• ranges(d)

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Preliminaries

• Def4 Let r and s be two ranges. rlts ? start(r)
  lt start(s) v
• (start(r)start(s) ? finish(r) gt
  finish(s))
• Lemma1 Let R be a nonintersecting range set. If
  rnsØ for r, s ? R ,
• then the following are
  true
• 1 start(r) lt start(s) gt finish(r)
  finish(s).
• 2 finish(r) gt finish(s) gt start(r)
  start(s)

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(NHPRTs) BOB (Data structure)

• The data structure binary tree on binary tree
  (BOB) comprises a single balanced binary search
  tree at the top level
• Top-level balanced binary search tree is called
  the point search tree (PTST)
• Each node z of PTST, we associate a point,
  point(z). For every node z of PTST, node in the
  left subtree of z have smaller point values than
  point(z), and nodes in the right subtree of z
  have larger point values than point(z)

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(NHPRTs) BOB (Data structure)

• Let R be the set of nonintersecting ranges of the
  NHPRT.
• Each range of R is stored in exactly one of the
  nodes of the PTST
• The root of the PTST stores all ranges r ? R such
  that start(r) point(root) finish(r) all
  ranges r ? R such that finish(r) lt point(root)
  are stored in the left subtree of the root all
  ranges r ? R such that point(root) lt start(r) are
  stored in the right subtree of the root

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(NHPRTs) BOB (Data structure)
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(NHPRTs) BOB (Data structure)

• The number inside each node is point(z), and the
  outside each node, we give ranges(z)

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(NHPRTs) BOB (Data structure)

• The ranges in ranges(z) may be ordered using the
  lt relation of Def4. Using this lt relation, we put
  the ranges of ranges(z) into a red-black tree
  called the range search-tree or RST(z)
• Each node x of RST(z) stores exactly one range of
  ranges(z), we refer to this range as range(x)
• Every node y in the left (right) subtree of node
  x of RST(z) has range(y) lt range(x) (range(y) gt
  range(x))

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(NHPRTs) BOB (Data structure)

• Each node x stores the quantity mp(x), which is
  the maximum of the priorities of the ranges
  associated with the nodes in the subtree rooted
  at x
• When x is a leaf, mp(x) p(x), where
• p(x) priority(range(x)),
• and when x is not a leaf
• mp(x) maxmp(leftchild(x)),
  mp(rightchild(x)), p(x)

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(NHPRTs) BOB (Data structure)
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(NHPRTs) BOB (Data structure)

• Lemma 2
• Let z be a node in a PTST and let x be a node
  in RST(z).
• Let st(x) start(range(x)) and fn(x)
  finish(range(x))
• 1 for every node y in the right subtree of x,
  st(y) st(x)
• and fn(y) fn(x)
• 2 for every node y in the left subtree of x,
  st(y) st(x)
• and fn(y) fn(x)

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(NHPRTs) BOB (search for hpr(d))
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(NHPRTs) BOB (search for hpr(d))
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(NHPRTs) BOB (insert a range)
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(NHPRTs) BOB (complexity of BOB)

• Lookup O(lognlogmaxR)
• a destination address is matched by about 1
  prefix on average, the maximum number of prefixes
  that match a destination address is at most 6. we
  conclude that maxRlt6. so complexity of BOB on
  real router tables is O(logn) per operation
• Insert, delete gt O(logn)

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Highest Priority Prefix Table (HPPTs) PBOB

• Since maxRlt6 for real router-tables, we replace
  the RST in each node z of the BOB PTST with an
  array linear list. ALL(z) of pairs of the form
  (pLength, priority)
• The pairs in ALL(z) are in ascending order of
  pLength

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Longest Matching Prefix Tables (LMPTS) LMPBOB

• Using priority pLength
• Replace the array linear list that is stored in
  each node of the PTST by a W-bit vector,
  bit(z)i denotes the ith bit of the bit vector
  stored in node z of the PTST, bit(z)i1 iff
  ALL(z) has a prefix whose length is i

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Experiment and conclusion

• Memory usage

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Experiment and conclusion

• Search time

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Experiment and conclusion

• Insert time

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Experiment and conclusion

• Delete time